Modelling in Life Insurance – A Management Perspective

The present chapter describes the developments that the insurance system has undergone over the past four decades and that have been brought to their conclusion in new regulations representing no less than a spectacular paradigm shift. The new paradigm is compared with its immediate predecessor in a perspective guided by timeless questions: what are the objectives of insurance, and how can they be achieved efficiently? And, more specifically, is it all about investments, market valuation, and solvency of businesses? Or has it also got something to do with social security, broad insurance coverage, transparency, and cost awareness? It is argued here that regimes like Solvency II and International Financial Reporting Standards are just our time’s response to problems created by our time’s practices (and malpractices), and that a rethink may well lead to a partial reinstatement of the preceding paradigm and add to it innovative ways of realizing the very idea of insurance.

The latest developments of both prudential (Solvency II) and financial reporting (MCEV, IFRS) frameworks seem to consecrate market consistent valuation as a kind of paragon of insurance liabilities assessment. In this chapter, we initially try to analyze the underlying motivations of this evolution. We show that it results from an objective of harmonization of measurement of quite different insurance contrats. This heterogeneity being the result of heterogeneous national insurance regulations. In the second part, we analyze the limitations of this measurement principle. For that, we mobilize some of the arguments opposed to Fair Value Accounting. Moreover, we insist on the limitations resulting as well from the implementation issues as of their use in a risk management perspective.

The cash flow projection model is simulating the way the insurance undertaking is working and reflects it by generating run-off balance sheets and P&Ls. This simulation implies a very thorough and deep understanding of all dimensions: products, assets, risk factors, markets, environments, regulations, behaviors, accounting... The challenge for the model is then to look at the whole undertaking “through the eyes of the management” and to encapsulate it and how things interact into formulas. This could only be done with a certain level of shortcuts: granularity of projected portfolios, behavioral laws…, in order both to reach acceptable running time and to be sustained by the IT capabilities. However these shortcuts should be carefully tailored so as not to false the results. Difficulties addressed in the article cover: the simulation of French multi-funds savings contracts where cash dynamically flows from General Fund to Unit-Linked funds (and vice versa), the granularity of asset classes, the simulation of structural cash flows from liabilities and notably the estimation of expenses, the stochastic modeling of assets, the determination of behavioral laws: policyholders’ profit sharing, surrenders, fund shifting, investment policy, behavior in central scenarios versus behavior in extreme scenarios… Answers to these difficulties should take into account the requirements of consistency (backtesting), reality (how the model reflects the risk profile of the undertaking), rapidity (a model is designed to be used in production under deadline’s constraint).

The projection of economic and financial risk factors is a key element of prospective analyzes made by life insurers, both for the calculation of reserves under Solvency 2 and for the asset allocation and management of financial risks. This projection is achieved in practice through “economic scenario generators” (ESG), which are inputs for the calculus of the economic value of assets and liabilities and the analysis of the distribution of this value. The calculation of economic values is based on the “no free lunch” assumption and therefore leads to model the risk factors in a riskneutral probability, while the analysis of the distribution of these values requires the projection of these factors under the historical probability. Therefore, the insurer must handle different representations of the risk factors, which requires looking at the characteristics of a risk neutral ESG, those of an “historical” one and the possible need for coherence between these two representations. This is what we propose to do in this chapter.

Pillar 1 of Solvency II framework set out quantitative requirements for calculation of the Best Estimate (BE) of liabilities and the Solvency Capital Requirement (SCR) (a 99.5 % value-at-risk measure for net assets over one year) using either a standard formula given by the regulators or an internal model developed by the insurance company. Its implementation for a life insurance company leads to complex cash flows projection models that aim to allow an accurate calculation of the BE (the SCR is most often determined using the standard formula). Meanwhile, the Own Risk and Solvency Assessment of Pillar 2 left the insurance company to define an optimal entity-specific solvency constraint on a multi-year time horizon. Its implementation requires in particular to model the distortion of the distribution of the entity’s coverage ratio over the period of the strategic plan. For this, it is needed to use much more aggregated models for the insurance company, not only to take into account computation and time constraints but also to ensure a minimum robustness to projections. Therefore, models adapted to these constraints are developed within a framework of probabilistic approaches and scenario analysis. The insurer is faced with the need to coordinate these aggregated models with the analytical view of Pillar 1. We propose in this chapter to discuss and challenge the way to bring back together models needed for the quantitative requirements of Pillar 1 with quality requirements of global and appropriate risk management system of Pillar 2.

Financial modelling is an art as well as a science. In the Life Insurance world it is pushed to the utmost complexity, requiring exacting work and long term collaboration of many skilled professionals. Alas, it is only half the story: software development is the other face of modelling. It should be the easier part, but that's far from beeing guaranteed.

As the famous statistician George Box said, “All models are wrong, but some of them are useful”. The goal of the validation process is not to say whether a model is right or wrong. Besides, model elaboration and validation must be regarded as an ongoing process, whose goal is to continuously improve and update the model. In this chapter, we shall focus on several aspects: the formal a priori validation process, back-testing issues and model risk assessment.

Insurance companies have increasingly used quantitative decision-making tools for a number of years. They have routinely taken advantage of models for a large number of business activities (underwriting policies, transferring risks, determining reserve adequacy, managing assets and liabilities, valuing risk exposures and financial instruments,..), but they now appeal to models for more ambitious ends like development of new products or strategic planning. Moreover, the new quantitative regulatory requirements of Solvency II, as well as various stakeholders’ expectations (including rating agencies, analysts, financial markets,...) push companies to develop more and more sophisticated models, not only for more complex products, but also for improved enterprise risk management. The expanding use of models reflects the range to which models can improve business decisions. But they also can lead to wrong decisions and potential adverse consequences when they are incorrect or misused, which is known as model risk. An active management that addresses these consequences has to be organised by insurance companies. In this chapter, we first try to understand what model risk is. In a second part, we discuss several approaches to measure model risk. In a third part, we raise the problem of model risk management and present several procedures to mitigate it. In a last part, we discuss the issue of model risk for the new regulatory framework Solvency II.

Rather than considering a “model” as a one-piece object, we can translate and adapt the concept of meta-models, commonly used in computer science, to the field of insurance management. We actually deal with a number of interconnected models. These models involve common concepts such as risk and value, assets and liabilities, reserves, management actions, etc. To avoid cacophonies (i.e. operational inefficiencies), every piece has to be placed in the right order. Depending on objectives and context, different levels of modelling will be required. Coherence in the modelling process does not mean uniformity. It is vital to understand correctly how models can effectively enhance business performance, yet not be blurred by undue complexity.

As seen in previous chapters of this book, models assess, over a long term projection period, future cash flows in different scenarios with various types of data. Their results are used by top managers to make important decisions at the Company level. Obviously feeding those models is a big issue to be addressed. Moreover, as the saying goes “garbage in, garbage out”, meaning that the quality of results is directly related to the quality of data. So data quality is a vital subject for many top managers of insurance undertakings (life and non life as well as mutual), because they need to trust in risk models results and use them in their decision making process. The article covers all the major questions related to data quality that you may have. In particular, it explains why data quality should be considered as a process and not a commando-like operation, because there is no absolute level of quality and because after the targeted level of data quality is achieved, it has to be maintained at this level in a changing environment. Firstly the article focuses on data definition (contract and asset information, endogenous or exogenous parameters for example), existing standards, best practices that can be put in place by the Company, and on the data life cycle that need to be well understood and mastered by top management. Secondly, the article elaborates also the advantages of the launch of data quality projects, the building of clear data quality governance and of an optimal documentation. The article focuses on the importance of beginning on a well-defined and representative perimeter in order to experience the method, to achieve in a constrained period of time and after that, to increase the perimeter of data on which the process of quality has to be put in place. The article also considers existing solutions proposed by the market such as packaged data management solutions.

Managing is deciding. Today no decision is made in the insurance world without using models. Decision-makers are facing many challenges in this situation: models might evolve from entity-specific to standardized under the pressure of regulators and the lack of diversity of providers, being less relevant and trigerring unintended sheep-like behaviours. Models are good at simulating the future from the past but they fail to simulate the unexpected non-linear phenomenon. Often more than one model is used but their consistency is not guaranteed. Understanding the model is a key issue for decision-makers. Models say what a pure rational based decision should be ignoring strategy and politics, discarding the true beliefs of the person making the decision. Models could not duplicate the decision-making process; however they could be the Fifth Solvency II key function.

Stakeholders’ behaviour has several impacts on model risk and model management. The asset side of the balance sheet may be impacted by feedback loops on financial markets. Customer behaviour is one of the top risks faced by a company. Consequently, it must be carefully addressed in the model. In addition to these behavioural risks that have to be taken into account in the models, we also study in this chapter the behaviour of decision-makers of the company through their attitudes with respect to risk and with respect to models.